At max G (6) the instantaneous turn has the same rate of turn, but the flight path will be different due to loss of speed. Slower speed while still maintaining the same G load meas a smaller turning circle. At high speeds and G, due to the inability of the planes to maintain a flat turn at constant speed, the flight path does not look like a circle - it is more of a spiral like a snail shell.
The AH pilots are limited at 6G, so this is what the plane can maintain till the speed drops below the critical speed at which the plane cannot pull 6Gs anymore. From that point on, the limit is the maximum lift of the plane relative to its weight - generally this means that a low wingloading is preferable for maintaining the turn RATE. High wingloading means that in order to maintain the 6Gs, the planes needs higher AoA and hence it produces more drag - and slows down faster. At high speeds in unsustained turns, low wingloading is "wasted" since the wings are not producing their max potential lift anyway due to the pilot limits. And here comes the distinction between the turn rate and turn radius. The plane that can slow down faster will enjoy the smaller turning circle. The plane that can maintain 6Gs longer will enjoy a better turning rate over time. Who will "out turn" who depends entirely on the geometry of the battle. This is why high wingloading planes can still be good dogfighters - as long as the fight is at high speeds.
From the planes mentioned in the above posts, the P47 and Typhoon dump a lot of energy very fast in a turn. Responsive elevators, a dragy airframe and the ability to pull very high AoA without snap stalling are good features for this purpose. This means that they can pull a very tight "corner" (the shape of the flight path) without much rate-of-turn disadvantage, as long as the speed is high enough. But after 90 to 180 degrees, the have lost so much speed that they are now at a severe disadvantage against most planes if the turning continues and they cannot trade alt to gain speed again. However, that initial fast and tight turn can place them at an advantageous position for the next move. This is how Jugs can beat spitfires in a fight, but they have to kill it in 1 or 2 moves or they will become disadvantaged.
In R/L, jugs were designed to dogfight at high alts. There, the option to trade alt for speed is almost always open. This meant that the jug could pull one or two tight corners and then dive to regain speed before it got caught too slow to turn. At high alts dogfights did not typically involve very elaborate ACM. Pilots would try a move or two and if that did not go well, the next thing would have been a split-S and a screaming dive to the safety of the clouds. Jugs are kings of the all-or-nothing corners, fast to roll in the split-S and excellent divers - this is why they did so well up high in the ETO, in spite of being initially ridiculed as 7 ton milk jugs.
